Can Intuition Replace Physics in Solving Structural Analysis Problems?

[tmer]

Hi,

Ive attached my attempt at solutions please help me resolve question 1a

thank you,

 

[PhanthomJay]

The beam is statically indeterminate, so you need more than just the equilibrium equations to solve it. Using just the equilibrium equations won't cut it. Your shear and moment diagrams are conceptually incorrect; you have ignored the reaction force at B.

 

[tmer]

The beam is statically indeterminate, so you need more than just the equilibrium equations to solve it.

How do you deduce that?

Using just the equilibrium equations won't cut it. Your shear and moment diagrams are conceptually incorrect; you have ignored the reaction force at B.

so there should be a jump at point B in the sheer force diagram. What would the bending moment diagram look like?

 

[SolidElast]

The beam is statically indeterminate, so you need more than just the equilibrium equations to solve it. Using just the equilibrium equations won't cut it. Your shear and moment diagrams are conceptually incorrect; you have ignored the reaction force at B.

I agree absolutely.
What way it requires to fix undetermination? Different approaches are possible. I can try to solve but it is not so fast.
Try to find here in the meantime http://www.orlovsoft.com/mmsamples/mmpage01.html

 

[SolidElast]

The first Case:
http://img705.imageshack.us/img705/9721/tophysicsforum03.png
The second Case:
http://img29.imageshack.us/img29/1944/tophysicsforum04.png
Both together:
http://img824.imageshack.us/img824/9440/tophysicsforum05.png
I hope it helps. But if you need equations post here, I will try.

 

[tmer]

thank you SolidElast, but how did you get the numbers 18000,60000 for first case?

 

[SolidElast]

For example, by Force Method. Be patient, it is simple but not is so obviously. You need only in physics process understanding. Your first task in general kind looks like this.
http://img823.imageshack.us/img823/2784/tophysicsforum06.png
According to Hook Rule (liner deformations) we can apply superposition principle.
So, detected task is presented by two separate tasks superposition.
http://img513.imageshack.us/img513/6137/tophysicsforum07.png
And
http://img38.imageshack.us/img38/7364/tophysicsforum08.png
Now we can remember that total deflection in B point is zero:

${\it wIScheme}_{{B}}+{\it wIIScheme}_{{B}}=0$
From last equation we determine unknown $R_{{B}}$

 

[tmer]

I don't understand, what is wISchemeB, wIISchemeB ?

Is the pink line the bending moment of the beam?

 

[SolidElast]

Deflections. The solution's main idea is fact that deflection of B point (for example B) is zero because there is fixing. The way is to combine equation of such fact.

 

[pongo38]

Although previous helpers are correct, there is another interpretation of the badly worded question part a i). If it had said "draw the approximate deflected shape and the approximate bending moment diagram", you could have done that without any physics. Maybe just an intuitive answer is possible, and worth 8 marks if you understand the relationship between types of support, loading, deflected shape and M diagram. Then, in part (ii) the points of contraflexure are given. This unlocks the indeterminacy and enables you to draw the moment and shear diagrams without indeterminate analysis. Symmetry also helps understanding in this question.